Séminaires : Groupes, Représentations et Géométrie

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Given a non-commutative algebra that is a finite module over a finitely generated center, we construct the Lafforgue variety, an affine scheme equipped with an open dense subscheme whose geometric points parametrize the simple modules of that algebra. We will also study the behavior of the Lafforgue variety under deformations of the algebra. In particular, we will report on partial progress on a conjecture by Aubert, Baum and Plymen asserting the existence of a flat deformation between the reducibility loci of different specializations of an affine Hecke algebra.